Best Known (39, 39+67, s)-Nets in Base 7
(39, 39+67, 40)-Net over F7 — Constructive and digital
Digital (39, 106, 40)-net over F7, using
- net from sequence [i] based on digital (39, 39)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 39)-sequence over F49, using
- s-reduction based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- s-reduction based on digital (0, 49)-sequence over F49, using
- base reduction for sequences [i] based on digital (0, 39)-sequence over F49, using
(39, 39+67, 96)-Net over F7 — Digital
Digital (39, 106, 96)-net over F7, using
- t-expansion [i] based on digital (33, 106, 96)-net over F7, using
- net from sequence [i] based on digital (33, 95)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 33 and N(F) ≥ 96, using
- net from sequence [i] based on digital (33, 95)-sequence over F7, using
(39, 39+67, 1050)-Net in Base 7 — Upper bound on s
There is no (39, 106, 1051)-net in base 7, because
- 1 times m-reduction [i] would yield (39, 105, 1051)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 55155 430902 623175 452309 923149 079592 397421 699743 810477 928587 210921 858695 058145 007931 587299 > 7105 [i]